We discuss two aspects of nonlinear propagation of fiber gratings. The first of these is grating solitons, which were recently observed experimentally. Grating solitons exist because of the balancing of nonlinearity and grating dispersion. The second is the nonlinear interaction occuring when a strong pump pulse and a weak signal pulse copropagate through a grating. This is predicted to lead to pulse compression and enhanced parametric amplification of the signal pulse. Although these latter effects have not yet been observed experimentally, the required parameters are comparable to those for observing grating solitons.